Dimiter Zlatanov

Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified.

Constraint Singularities as C-Space Singularities

This paper examines the phenomenon of constraint singularity of a parallel mechanism, as defined in a recent publication. We focus our attention on the fact that constraint singularities are always singular points of the configuration space of the kinematic chain. As such, they separate distinct configuration space regions and may allow transitions between dramatically different operation modes. All this is exemplified by a multi-operational parallel mechanism that can undergo a variety of transformations when passing through singular configurations.

Analytical kinematics models and special geometries of a class of 4-DOF parallel mechanisms

The paper discusses forward and inverse kinematics of a class of four-degree-of-freedom (DOF), four-legged parallel mechanisms providing three rotational and one translational DOFs. A fully parametric analytical form solution to the inverse-position problem is provided. All working modes of the mechanism are shown and discussed. The equations of the forward-position problem are obtained under different leg arrangements, and a numerical example is provided. New special geometries in the class are proposed, including one suitable for keyhole surgery.

Kinematics Analysis of the Exechon Tripod

The Exechon 5-Axis Parallel Kinematic Machine (PKM) is a successful design created in Sweden and adopted by many producers of machine tools around the world. A new version of the manipulator is being developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The basic Exechon architecture consists of a 3-degree-of-freedom (dof) parallel mechanism (PM) connected in series with a two- or three-dof spherical wrist. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper presents the kinematic analysis of both the PM and the hybrid parallel-serial architecture. We describe the complex three-dimensional motion pattern of the PM platform, derive the kinematic equations and provide explicit solutions for the inverse kinematics.Copyright

Numerical computation of manipulator singularities

This paper provides a method to compute all types of singularities of non-redundant manipulators with non-helical lower pairs and designated instantaneous input and output speeds. A system of equations describing each singularity type is given. Using a numerical method based on linear relaxations, the configurations in each type are computed independently. The method is general and complete: it can be applied to manipulators with arbitrary geometry; and will isolate singularities with the desired accuracy. As an example, the entire singularity set and its complete classification are computed for a two-degree-of-freedom mechanism. The complex partition of the configuration space by various singularities is illustrated by three-dimensional projections.

SwarmItFIX: a multi‐robot‐based reconfigurable fixture

Purpose – The use of thin sheets with 3D geometries is growing in quantity, due to current progress towards life‐cycle design and sustainable production, and growing in geometrical complexity, due to aesthetic and quality concerns. The growth in manufacturing equipment flexibility has not kept pace with these trends. The purpose of this paper is to propose a new reconfigurable fixture to shorten this gap.Design/methodology/approach – The design implements a novel concept of fixturing. Without interrupting the machining process, a swarm of adaptable mobile agents periodically reposition and reconfigure to support the thin‐sheet workpiece near the tool‐point. The technology has been developed by adopting a multi‐disciplinary, life‐cycle approach. Modularity and eco‐sustainability paradigms have informed the design.Findings – The performance of the physical prototype in an industrial scenario is highly satisfactory. Experiments demonstrate the ability of the system to reconfigure while maintaining machining ...

A General Method for the Numerical Computation of Manipulator Singularity Sets

The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.

A hierarchical CSP search for path planning of cooperating self-reconfigurable mobile fixtures

The paper presents the application of artificial intelligence tools for the path planning of complex multi-agent robotic systems. In particular, a solution is proposed to the planning problem for the conjoint operation of two or more mobile robotic fixtures used for the manufacturing of large workpieces, like those used in the aerospace industry. Such fixturing systems have been recently designed and tested, raising hopes to better satisfy the dynamic conditions of modern manufacturing, with its increasing emphasis on flexibility, adaptability, and automation. The proposed planning method is novel in two fundamental aspects. First, it interprets planning as a constraint satisfaction problem (CSP), rather than as a constrained optimisation, an approach ubiquitous in the path and motion planning literature. Secondly, the formulated CSP is solved by a hierarchy of incremental state space search algorithms which differ in some way from the existing state of the art. This hierarchy includes levels related to the robot and workpiece arrangement parameters and to three components of mobile fixture agents: a supporting head, a mobile base, and a parallel manipulator, respectively. Due to the use of CSP search, the planner constitutes a largely application-independent framework, on the basis of which specific industrial implementations can be defined by supplying the relevant physical, geometrical, and time-related constraints.

Kinematic Analysis of a Meso-Scale Parallel Robot for Laser Phonomicrosurgery

The paper presents the kinematic model of a new meso-scale (\(\sim \)1 cm\(^3\)) parallel kinematic machine intended for laser phono-microsurgery of the vocal folds. The proposed mechanism uses the displacement generated by piezoelectric cantilever actuators manufactured via a Smart Composite Microstructure technique. The architecture, the geometry, and the position kinematics of the device, modeled as a spatial linkage, are discussed briefly. Then, the paper presents a velocity and singularity analysis and concludes that the new meso-scale parallel kinematic machine does not have singularities in the neighborhood of the reference configuration where it is required to operate.

Constraint and Singularity Analysis of the Exechon Tripod

The paper discusses mobility and singularities of the Exechon three-degree-of-freedom (dof) parallel mechanism (PM) on which a family of parallel kinematic machines is based. Exechon designs are used by a number of machine-tool makers. A new version of the manipulator has been developed as a component of a mobile self-reconfigurable fixture system within an inter-European project. The PM has two UPR (4-dof) legs, constrained to move in a common rotating plane, and an SPR (5-dof) leg. The paper focuses on the constraint and singularity analysis of the mechanism. The screw systems of end-effector freedoms and constraints are identified. The singular configurations are classified in detail and their geometric interpretation is discussed. The velocity kinematics and the Jacobian operator are formulated via a screw-system approach. A fully parameterized package of Maple tools has been developed and used to visualize singularities and their consequences.Copyright